Chapter 18: Circuits and Circuit Elements1
Section 1: Schematic Diagrams and Circuits
Schematic Diagrams
Schematic diagram: diagram that depicts the construction of an electrical apparatus

Uses symbols to represent circuit elements
o Battery, light bulbs or lamps, resistors, switch, capacitor
Chapter 18: Circuits and Circuit Elements2
Electric circuits
How a light bulb works …
1. A wire connects the terminals of the battery to the light bulb
2. Charges build up on one terminal of the battery and follow the path (through the
light bulb) to reach the other terminal
3. Charges are moving through the wire, so a current exists
4. The current causes the filament (a resistor to the current) to heat up and glow
Electric circuit: a path through which charges can flow

Schematic diagram for a circuit is also called a circuit diagram
Load: Any element or group of elements in a circuit that dissipates energy

Simple circuit consists of a potential difference source (battery) and a load (bulb
or group of bulbs)
o Wires have negligible resistance, so are not considered a load.
Closed circuit: closed-loop path for electrons to follow
Open circuit: no complete path (switch open, bulb blown); charges cannot flow,
therefore no current (I=0).
Short circuit: situation where a wire connects the terminals of a battery


low resistance
dangerous – increase in current may cause the wires to overheat. Wire’s
insulation may melt or cause a fire
Source of potential difference
Terminal voltage
No battery (or other source of electricity), no
charge flow, and no current


Battery is the source of potential
difference and electrical energy for
the circuit
o Any device that increases
potential energy of charges is a
source of emf (originally stood
for electromotive force)
 Energy per unit charge
supplied by a source of
electric current
 Charge pump for pushing
electrons in one direction



Batteries have internal resistance
caused by the charges colliding
with atoms inside the battery
Terminal voltage (potential
difference across the battery’s
terminals) is less than emf
Charges move through a circuit and
electrical potential energy is
converted to other types of energy
(light, sound, heat)
Energy is conserved – energy
gained from the battery must equal
energy dissipated through the load
Chapter 18: Circuits and Circuit Elements3
Section 2: Resistors in Series or in Parallel
Resistors in series
Simple circuit consisting of 1 bulb and a
battery





Potential difference across the bulb
equals the terminal voltage
Total current can be found using ΔV=IR
When a second bulb is added to the
circuit, charges must pass through the
first bulb before going through the second
bulb.
All charges follow the same conducting
path – bulbs are connected in series
Charge is conserved; charges cannot build
up or disappear at one point
o Amount of charge entering and
exiting the first bulb equals the
amount of charge entering and
exiting the second bulb
o Current in the 1st bulb = current in
the 2nd bulb
o When many resistors are connected
in series, the current in each
resistor is the same.
Remember from section 1 – potential
difference across the battery must equal
potential difference across the load  here,
ΔV = ΔV1 + ΔV2 (potential difference across
each resistor).
Equivalent resistance
Total current in a series circuit depends
on how many resistors are present and
the resistance in each.




ΔV = I1R1 + I2R2  ΔV = I(R1 + R2)  ΔV=IReq

To calculate the potential difference across
each resistor


Current in each resistor is equal to
total current
ΔV = I1R1 and ΔV = I2R2, using the
resistance of each resistor

To find the total current, you
first have to find the total
resistance of the circuit
(equivalent resistance)
Then, using ΔV=IReq, you can find
the current in the series.
Req = R1 + R2 + R3 + …. Rn
Equivalent resistance equals the
total of individual resistances in
series.
Equivalent resistance of a series
combination of resistors is always
greater than any individual
resistance.
I = ΔV
Req
Chapter 18: Circuits and Circuit Elements4
Sample 18A
A 9.0 V battery is connected to four light bulbs, as shown below. Find the equivalent
resistance for the circuit and the current in the circuit.
In series … we must all do our part!
If a single bulb burns out, there is a gap in the conducting pathway

Open circuit, no current, no light!
Why a series circuit?





Regulate current in a device
Each additional bulb decreases current in each bulb
Each filament will not have to withstand a high current
Several smaller resistors can be added to a much greater resistance that might
not be available
May be advantageous to have a circuit where there isn’t any current if one
component fails (burglar alarms)
Resistors in Parallel



Wiring arrangement that provides
alternative pathways for movement of
charge
Resistors in parallel all have the same
potential difference, and all have
terminal voltage of the battery
Current varies in each resistor
Chapter 18: Circuits and Circuit Elements5
More about current in parallel circuits and equivalent resistance








Multiple paths for charges to go
o some charge moves through the top path
o some charge moves through the bottom path
If one of the bulbs has less resistance, more charges will flow through that path
(going through the path of least resistance)
Sum of the currents in each bulb equals the current delivered by the battery
o I = I1 + I2 + I3 …
According to Ohm’s Law,
I = ∆V = ∆V1 + ∆V2
Req R1 R2
Because ∆V is the same across each bulb in a parallel circuit, divide both sides by
∆V.
1 = 1 + 1
Req R1 R2
Equivalent resistance in parallel is calculated using a reciprocal relationship
Equivalent resistance for a parallel arrangement of resistors must always be less
than the smallest resistance in the group of resistors.
Note: Parallel
Sample Problem 18B
circuits do not
require all elements
to operate.
A 9.0 V battery is connected to four resistors, as shown below.
Find the equivalent resistance for the circuit and the total current in the circuit.
Chapter 18: Circuits and Circuit Elements6
Section 3: Complex Resistors Combinations
Resistors combined both in parallel and in
series
Equivalent resistance for a circuit

Series and parallel circuits are not usually
found independent of each other

Most circuits use both types of
wiring for the different advantages
Examples


Home fuse box or circuit breaker is
wired in series for many outlets
o Keeps the loads from getting
too high
o if current becomes too high,
either the fuse blows, or the
circuit trips interrupting the
current
Outlets tend to be wired in parallel
Fuse or circuit breaker (CB) is wired
in series
o Current of the fuse (or CB) is
the same as the total current
in the circuit
o To find current, you have to
find equivalent resistance
first.
Equivalent resistance of a complex
circuit


Simplify the circuit into groups of
series and parallel resistors
Find the Req for each group using
rules already established.
Sample Problem 18C
Determine the equivalent resistance of the complex circuit shown below:
Chapter 18: Circuits and Circuit Elements7
Finding current and potential difference
Once you have found equivalent resistance, work backward to find current in and
potential difference across any resistor in that circuit.
Examples:




In a household circuit, a fuse or circuit breaker is in series with the load.
Current is equal to total current.
Use ΔV=IR with potential difference and Req to find current.
Once current is found, you can then find potential difference across each
individual load or the fuse/circuit breaker.
Sample Problem 18D
Determine the current in and potential difference across the 2.0 Ω resistor highlighted in
the figure below.